The captain has been sidelined since early October with a knee problem, a setback that forced Mikel Arteta to rethink his midfield structure during a period in which the league leaders have been juggling multiple fitness concerns.
In Odegaard's absence, Arsenal have relied heavily on Declan Rice's consistency at the base of midfield, while new 60-million-pound signing Eberechi Eze has stepped into the creative role normally occupied by the Norwegian.
The reshuffle has helped keep Arsenal at the top of the Premier League, but the prospect of Odegaard returning sooner than originally projected offers a timely boost as the fixtures begin to intensify.
"It's moving forward. The match today [Sunday] came a little too early," said Odegaard, via TV2.
"But it's starting to look better, so hopefully I'll be back soon."
The club's wider injury situation, however, remains a major worry. Arsenal are in the middle of an injury crisis that has seen Viktor Gyokeres, Noni Madueke and Odegaard all sidelined in recent weeks.
Gabriel Martinelli and Kai Havertz have also missed matches, further stretching Arteta's squad.
Concerns deepened at the weekend when defender Gabriel limped off while representing Brazil at the Emirates.
Meanwhile, Riccardo Calafiori caused alarm for Italy after leaving their camp with a hip issue, though early indications suggest he is expected to be fit for Arsenal's next outing.
